Online Classes See Cheating Go High-Tech" underscores the importance of having multiple measures of assessment in an online class AND making some of those measures project based so that a student’s work and skill set becomes recognizable.
The Cuyamaca College "Best Practices Checklist for Effective Online Instruction" lists several ways to reduce cheating. In particular we encourage "Instructors use more than one method to assess student learning, and the methods are appropriate to the content being assessed. (item 3.4)"
Another Checklist item that is applicable is "Learning activities foster instructor-student, content-student, and if appropriate to the course, student-student interaction (e.g. e-mail, discussion, phone, online conferences)." (item 5.1)
The more instructors get to know their students through discussion and other interactive assignments and activities, the easier it will be to determine when a student is not doing their own work.